Related papers: Canonical contact unit cotangent bundle
We define a subcategory of the category of diffeological spaces, which contains smooth manifolds, the diffeomorphism subgroups and its coadjoint orbits. In these spaces we construct a tangent bundle, vector fields and a de Rham cohomology.
We produce an example of a rigid, but not infinitesimally rigid smooth compact complex surface with ample canonical bundle using results about arrangements of lines inspired by work of Hirzebruch, Kapovich and Millson, Manetti and Vakil.
Motivated by the holographic prescriptions for computing entanglement entropy and complexity, we study the properties of volumes/areas of bulk surfaces. We obtain a simple formula for the shape dependence of holographic entanglement entropy…
We define contact fiber bundles and investigate conditions for the existence of contact structures on the total space of such a bundle. The results are analogous to minimal coupling in symplectic geometry. The two applications are…
This is an exposition of the inverse spectral theory of canonical systems based on de Branges spaces of entire functions
We endow the cohomology of configuration spaces of a manifold with a product arising from superposing configurations. We prove that, under the scanning isomorphism, this product corresponds to the cup-product of the section space of the…
We present a two-part program for state space decomposition. States are classified into entanglement classes based on local unitary transformations, and then characterized as elements of topological spaces using the language of fibre…
Complex band structure generalizes conventional band structure by also considering wavevectors with complex components. In this way, complex band structure describes both the bulk-propagating states from conventional band structure and the…
We investigate the relation between Cartan decompositions of the unitary group and discrete quantum symmetries. To every Cartan decomposition there corresponds a quantum symmetry which is the identity when applied twice. As an application,…
Let $h$ be a without fixed point lift to the plane of a homeomorphism of the open annulus isotopic to the identity and without wandering point. We show that $h$ admits a $h$-invariant dense open set $O$ on which it is conjugate to a…
In this article we prove the existence of a canonical theta structure for the canonical lift of an ordinary abelian variety.
The paper describes a cover of the future cover of a sofic shift which is canonical in the same way as the future cover itself. In some cases the cover is isomorphic to the future cover and in other it is a genuine extension.
We study contact resolutions of Jacobi structures which are contact on an open subset. We give several classes of examples, as well as classes for which it cannot exist.
We show that on any closed contact manifold of dimension greater than 1 a contact structure with vanishing contact homology can be constructed. The basic idea for the construction comes from Giroux. We use a special open book decomposition…
A formal system called cologic is proposed for the study of compacta. A counterpart of countable model theory is developed for this system, and it is applied to model theory of the pseudo-arc.
On the basis of the covariant description of the canonical formalism for quantization, we present the basic elements of the symplectic geometry for a restricted class of topological defects propagating on a curved background spacetime. We…
We describe a technique for structured prediction, based on canonical correlation analysis. Our learning algorithm finds two projections for the input and the output spaces that aim at projecting a given input and its correct output into…
We study neighborhoods of configurations of symplectic surfaces in symplectic 4-manifolds. We show that suitably `positive' configurations have neighborhoods with concave boundaries and we explicitly describe open book decompositions of the…
In this paper we write explicitly the open book decompositions of links of quotient surface singularities supporting the corresponding unique Milnor fillable contact structure. The page-genus of these Milnor open books are minimal among all…
We introduce a category of noncommutative bundles. To establish geometry in this category we construct suitable noncommutative differential calculi on these bundles and study their basic properties. Furthermore we define the notion of a…